The vast world of quantum advantage

TL;DR

This paper explores the fundamental properties and potential of quantum advantages across various fields, emphasizing the importance of mathematical tools and the possibility of unforeseen benefits in future quantum technologies.

Contribution

It introduces five key properties defining ideal quantum advantages and discusses the inherent unpredictability of some advantages, highlighting the vast, largely unexplored landscape of quantum benefits.

Findings

Some quantum advantages are inherently unpredictable classically.

Mathematical tools are essential for navigating quantum advantage landscape.

Future quantum technologies may reveal advantages beyond current imagination.

Abstract

The quest to identify quantum advantages lies at the heart of quantum technology. While quantum devices promise extraordinary capabilities, from exponential computational speedups to unprecedented measurement precision, distinguishing genuine advantages from mere illusions remains a formidable challenge. In this endeavor, quantum theorists are like prophets attempting to foretell the future, yet the boundary between visionary insight and unfounded fantasy is perilously thin. In this perspective, we examine our mathematical tools for navigating the vast world of quantum advantages across computation, learning, sensing, and communication. We explore five keystone properties: predictability, typicality, robustness, verifiability, and usefulness that define an ideal quantum advantage, and envision what new quantum advantages could arise in a future with ubiquitous quantum technology. We prove that some quantum advantages are inherently unpredictable using classical resources alone, suggesting a landscape far richer than what we can currently foresee. While mathematical rigor remains our indispensable guide, the ultimate power of quantum technologies may emerge from advantages we cannot yet conceive.